Meteorologist Ed Lorenz, pioneer of chaos theory, is well known for his demonstration of ‘the butterfly effect’. More fundamentally, however, Lorenz’s research established a profound link between space-time calculus and state-space fractal geometry. Amazingly, properties of Lorenz’s fractal invariant set can be shown to relate space-time calculus to deep areas of mathematics associated with Wiles’ proof of Fermat’s Last Theorem and G ̈odel’s Incompleteness Theorem. Motivated by this, it is proposed that our theories of fundamental physics should also be framed in terms of state-space geometry rather than the traditional space-time calculus. To develop these ideas more concretely, it is supposed that the universe U is itself a deterministic dynamical system evolving on a fractal invariant set IU in its state space. Symbolic representations of IU are constructed explicitly based on permutation representations of quaternions. The resulting ‘Invariant Set Theory’ provides a conspiracy-free causal perspective on fundamental physics from which some key concepts in quantum theory are emergent: incompatible observables, wave-particle duality, Planck’s constant and apparent nonlocality; Bell’s theorem being nullified by exploiting a finite-precision loophole arising from the fractal geometry of IU . The complex Hilbert Space of quantum theory emerges as a singular limit of this topological representation of IU . The primacy of geometry as embodied in the proposed theory extends the principles underpinning general relativity. As a result, the physical basis for contemporary programmes which seek a ‘quantum theory of gravity’ is questioned. Based on the geometry of IU , an alternative ‘gravitational theory of the quantum’ is proposed. Some meat is put on the bones of Penrose’s suggestion that the correct theory of quantum gravity might be a deterministic but non-computable theory. Sent from my iPad On Sep 10, 2013, at 11:51 PM, art wagner wrote: arxiv.org/pdf/1309.2396.pdf
Posted on: Wed, 11 Sep 2013 16:38:07 +0000
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